Question

Consider the number line with the plotted square roots.Inspect the number line. Which square roots have a difference of about 0.5?(1 point)Responses11−−√ and 14−−√square root of 11 and square root of 1411−−√ and 19−−√ square root of 11 and square root of 1919−−√ and 24−−√ square root of 19 and square root of 2414−−√ and 19−−√

Answer 1

To find the square roots that have a difference of about 0.5, we can approximate the square roots of the numbers given and then calculate their differences.

1. **√11** ≈ 3.32
2. **√14** ≈ 3.74
- Difference: |√14 - √11| ≈ |3.74 - 3.32| ≈ 0.42 (about 0.5)

3. **√19** ≈ 4.36
- Difference: |√19 - √11| ≈ |4.36 - 3.32| ≈ 1.04 (not close to 0.5)
- Difference: |√19 - √14| ≈ |4.36 - 3.74| ≈ 0.62 (not quite 0.5)

4. **√24** ≈ 4.90
- Difference: |√24 - √19| ≈ |4.90 - 4.36| ≈ 0.54 (close to 0.5)

From these calculations, the pairs that seem to have a difference around 0.5 are:

- **√11 and √14** (Difference ≈ 0.42)
- **√19 and √24** (Difference ≈ 0.54)

Thus, the correct responses regarding the square roots that have a difference of about 0.5 are:

- √11 and √14 (square root of 11 and square root of 14)
- √19 and √24 (square root of 19 and square root of 24)

However, if we have to select one option from those provided in the initial list you shared, **√11 and √14** is the best choice since it is closest to 0.5.